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Answers
Step-by-step explanation:
Given :-
Let R1 and R2 be the remainders when the polynomials f(x) = x³+2ax²-5x-7 and
g(x) = x³+x²-12x+6a are divided by (x+1) and (x-2) respectively.
To find :-
If 2R1 + R2 = 12 Find the value of a ?
Solution :-
Given that
Given polynomials are f(x) = x³+2ax²-5x-7 and
g(x) = x³+x²-12x+6a
Given divisors = (x+1) and (x-2)
If f(x) = x³+2ax²-5x-7 is divided by (x+1) then
By Remainder Theorem
The remainder is f(-1)
According to the given problem
f(-1) = R1
=> (-1)³+2a(-1)²-5(-1)-7 = R1
=> R1 = -1+2a(1)+5-7
=> R1 = -1+2a-2
=> R1 = 2a-3 ----------------(1)
and
If g(x) = x³+x²-12x+6a is divided by (x-2) then
By Remainder Theorem
The remainder is g(2)
According to the given problem
g(2) = R2
=> 2³+(2)²-12(2)+6a = R2
=> R2 = 8+4-24+6a
=> R2 = 12-24+6a
=> R2 = 6a-12 ----------------(2)
Given that
2R1 + R2 = 12
From (1) & (2)
=> 2(2a-3) + (6a-12) = 12
=> 4a-6 + 6a-12 = 12
=> (4a+6a)+(-6-12) = 12
=> 10a-18 = 12
=> 10a = 12+18
=> 10a = 30
=> a = 30/10
=> a = 3
Therefore, a = 3
Answer:-
The value of a for the given problem is 3
Used Theorem :-
Remainder Theorem :-
Let P(x) be a polynomial of the degree greater than or equal to 1 and x-a is another linear polynomial, if P (x) is divided by x-a then the remainder is P(a) .
Answer:
no I can't solve this problem